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Theorem wom2 434
 Description: Weak orthomodular law for study of weakly orthomodular lattices.
Assertion
Ref Expression
wom2 a ≤ ((ab) ∪ ((ac) ≡ (bc)))

Proof of Theorem wom2
StepHypRef Expression
1 le1 146 . 2 a ≤ 1
2 conb 122 . . . . . 6 (ab) = (ab )
32ax-r4 37 . . . . 5 (ab) = (ab )
4 oran 87 . . . . . . 7 (ac) = (ac )
5 oran 87 . . . . . . 7 (bc) = (bc )
64, 52bi 99 . . . . . 6 ((ac) ≡ (bc)) = ((ac ) ≡ (bc ) )
7 conb 122 . . . . . . 7 ((ac ) ≡ (bc )) = ((ac ) ≡ (bc ) )
87ax-r1 35 . . . . . 6 ((ac ) ≡ (bc ) ) = ((ac ) ≡ (bc ))
96, 8ax-r2 36 . . . . 5 ((ac) ≡ (bc)) = ((ac ) ≡ (bc ))
103, 92or 72 . . . 4 ((ab) ∪ ((ac) ≡ (bc))) = ((ab ) ∪ ((ac ) ≡ (bc )))
11 ska4 433 . . . 4 ((ab ) ∪ ((ac ) ≡ (bc ))) = 1
1210, 11ax-r2 36 . . 3 ((ab) ∪ ((ac) ≡ (bc))) = 1
1312ax-r1 35 . 2 1 = ((ab) ∪ ((ac) ≡ (bc)))
141, 13lbtr 139 1 a ≤ ((ab) ∪ ((ac) ≡ (bc)))
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131  df-cmtr 134 This theorem is referenced by:  ka4ot  435
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